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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance (2nd ed.)\n",
    "\n",
    "**Mastering Data-Driven Finance**\n",
    "\n",
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/py4fi_2nd_shadow.png\" width=\"300px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistics (c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import datetime as dt\n",
    "from pylab import mpl, plt\n",
    "# import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "plt.style.use('seaborn')\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "np.random.seed(1000)\n",
    "np.set_printoptions(suppress=True, precision=4)\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples=250, centers=4,\n",
    "                  random_state=500, cluster_std=1.25)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "<Figure size 720x432 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], s=50);\n",
    "# plt.savefig('../../images/ch13/ml_plot_01.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-Means Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = KMeans(n_clusters=4, random_state=0)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=4, random_state=0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_kmeans = model.predict(X)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 3, 0, 1, 3, 3, 3, 0, 2, 2], dtype=int32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_kmeans[:12]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_kmeans,  cmap='coolwarm');\n",
    "# plt.savefig('../../images/ch13/ml_plot_02.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Mixtures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = GaussianMixture(n_components=4, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianMixture(n_components=4, random_state=0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_gm = model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 3, 0, 1, 3, 3, 3, 0, 2, 2])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_gm[:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y_gm == y_kmeans).all()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_classification(n_samples=n_samples, n_features=2, n_informative=2,\n",
    "                           n_redundant=0, n_repeated=0, random_state=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.6876, -0.7976],\n",
       "       [-0.4312, -0.7606],\n",
       "       [-1.4393, -1.2363],\n",
       "       [ 1.118 , -1.8682],\n",
       "       [ 0.0502,  0.659 ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[:5]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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     "metadata": {},
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    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x=X[:, 0], y=X[:, 1], c=y, cmap='coolwarm');\n",
    "# plt.savefig('../../images/ch13/ml_plot_03.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Naive Bayes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = GaussianNB()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianNB()"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0041, 0.9959],\n",
       "       [0.8534, 0.1466],\n",
       "       [0.9947, 0.0053],\n",
       "       [0.0182, 0.9818],\n",
       "       [0.5156, 0.4844]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(X).round(4)[:5]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = model.predict(X)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0,\n",
       "       0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
       "       0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,\n",
       "       0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True, False,  True,  True,  True,  True,\n",
       "        True, False,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True, False, False, False,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True, False,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True, False,  True, False,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True, False,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True, False,  True, False,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True, False,  True, False,  True,  True,  True,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred == y  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.87"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y, pred)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xc = X[y == pred]  \n",
    "Xf = X[y != pred]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x=Xc[:, 0], y=Xc[:, 1], c=y[y == pred],\n",
    "            marker='o', cmap='coolwarm')  \n",
    "plt.scatter(x=Xf[:, 0], y=Xf[:, 1], c=y[y != pred],\n",
    "            marker='x', cmap='coolwarm');  \n",
    "# plt.savefig('../../images/ch13/ml_plot_04.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression(C=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.011 , 0.989 ],\n",
       "       [0.7266, 0.2734],\n",
       "       [0.971 , 0.029 ],\n",
       "       [0.04  , 0.96  ],\n",
       "       [0.4843, 0.5157]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(X).round(4)[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xc = X[y == pred]\n",
    "Xf = X[y != pred]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x=Xc[:, 0], y=Xc[:, 1], c=y[y == pred],\n",
    "            marker='o', cmap='coolwarm')\n",
    "plt.scatter(x=Xf[:, 0], y=Xf[:, 1], c=y[y != pred],\n",
    "            marker='x', cmap='coolwarm');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = DecisionTreeClassifier(max_depth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(max_depth=1)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08, 0.92],\n",
       "       [0.92, 0.08],\n",
       "       [0.92, 0.08],\n",
       "       [0.08, 0.92],\n",
       "       [0.08, 0.92]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(X).round(4)[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.92"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xc = X[y == pred]\n",
    "Xf = X[y != pred]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
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     "metadata": {},
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   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x=Xc[:, 0], y=Xc[:, 1], c=y[y == pred],\n",
    "            marker='o', cmap='coolwarm')\n",
    "plt.scatter(x=Xf[:, 0], y=Xf[:, 1], c=y[y != pred],\n",
    "            marker='x', cmap='coolwarm');\n",
    "# plt.savefig('../../images/ch13/ml_plot_05.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   depth | accuracy\n",
      "--------------------\n",
      "       1 |     0.92\n",
      "       2 |     0.92\n",
      "       3 |     0.94\n",
      "       4 |     0.97\n",
      "       5 |     0.99\n",
      "       6 |     1.00\n"
     ]
    }
   ],
   "source": [
    "print('{:>8s} | {:8s}'.format('depth', 'accuracy'))\n",
    "print(20 * '-')\n",
    "for depth in range(1, 7):\n",
    "    model = DecisionTreeClassifier(max_depth=depth)\n",
    "    model.fit(X, y)\n",
    "    acc = accuracy_score(y, model.predict(X))\n",
    "    print('{:8d} | {:8.2f}'.format(depth, acc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deep Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = MLPClassifier(solver='lbfgs', alpha=1e-5, max_iter=500,\n",
    "                    hidden_layer_sizes=2 * [75], random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.3 s, sys: 566 ms, total: 1.87 s\n",
      "Wall time: 282 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLPClassifier(alpha=1e-05, hidden_layer_sizes=[75, 75], max_iter=500,\n",
       "              random_state=10, solver='lbfgs')"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0,\n",
       "       1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0,\n",
       "       0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1,\n",
       "       0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = model.predict(X)\n",
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Keras (instead of TensorFlow 1.x example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.keras.layers import Dense\n",
    "from tensorflow.keras.models import Sequential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.random.set_seed(1)\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "features = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(64, activation='relu', input_dim=features))\n",
    "model.add(Dense(1, activation='sigmoid'))\n",
    "model.compile(loss='binary_crossentropy', optimizer='rmsprop',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.6876, -0.7976],\n",
       "       [-0.4312, -0.7606],\n",
       "       [-1.4393, -1.2363],\n",
       "       [ 1.118 , -1.8682],\n",
       "       [ 0.0502,  0.659 ]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x17a361c70>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y, epochs=50, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4/4 [==============================] - 0s 922us/step - loss: 0.2449 - accuracy: 0.9100\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.24486945569515228, 0.9100000262260437]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.evaluate(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = np.where(model.predict(X) > 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0,\n",
       "       0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,\n",
       "       0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Transforms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.6876, -0.7976],\n",
       "       [-0.4312, -0.7606],\n",
       "       [-1.4393, -1.2363],\n",
       "       [ 1.118 , -1.8682],\n",
       "       [ 0.0502,  0.659 ]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.2881, -0.5489],\n",
       "       [-0.3384, -0.5216],\n",
       "       [-1.1122, -0.873 ],\n",
       "       [ 0.8509, -1.3399],\n",
       "       [ 0.0312,  0.5273]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xs = preprocessing.StandardScaler().fit_transform(X)  \n",
    "Xs[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.7262, 0.3563],\n",
       "       [0.3939, 0.3613],\n",
       "       [0.2358, 0.2973],\n",
       "       [0.6369, 0.2122],\n",
       "       [0.4694, 0.5523]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xm = preprocessing.MinMaxScaler().fit_transform(X)  \n",
    "Xm[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.6791, -0.3209],\n",
       "       [-0.3618, -0.6382],\n",
       "       [-0.5379, -0.4621],\n",
       "       [ 0.3744, -0.6256],\n",
       "       [ 0.0708,  0.9292]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xn1 = preprocessing.Normalizer(norm='l1').transform(X)  \n",
    "Xn1[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.9041, -0.4273],\n",
       "       [-0.4932, -0.8699],\n",
       "       [-0.7586, -0.6516],\n",
       "       [ 0.5135, -0.8581],\n",
       "       [ 0.076 ,  0.9971]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xn2 = preprocessing.Normalizer(norm='l2').transform(X)  \n",
    "Xn2[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "markers = ['o', '.', 'x', '^', 'v']\n",
    "data_sets = [X, Xs, Xm, Xn1, Xn2]\n",
    "labels = ['raw', 'standard', 'minmax', 'norm(1)', 'norm(2)']\n",
    "for x, m, l in zip(data_sets, markers, labels):\n",
    "    plt.scatter(x=x[:, 0], y=x[:, 1], c=y,\n",
    "            marker=m, cmap='coolwarm', label=l)\n",
    "plt.legend();\n",
    "# plt.savefig('../../images/ch13/ml_plot_06.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.6876, -0.7976],\n",
       "       [-0.4312, -0.7606],\n",
       "       [-1.4393, -1.2363],\n",
       "       [ 1.118 , -1.8682],\n",
       "       [ 0.0502,  0.659 ]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.],\n",
       "       [1., 0.],\n",
       "       [1., 1.]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xb = preprocessing.Binarizer().fit_transform(X)  \n",
    "Xb[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 ** 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 1],\n",
       "       [1, 1],\n",
       "       [0, 0],\n",
       "       [3, 0],\n",
       "       [2, 2]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xd = np.digitize(X, bins=[-1, 0, 1])  \n",
    "Xd[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4 ** 2  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train-Test Splits "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x, test_x, train_y, test_y = train_test_split(X, y, test_size=0.33,\n",
    "                                                    random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SVC(C=1, kernel='linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1, kernel='linear')"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(train_x, train_y)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_train = model.predict(train_x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9402985074626866"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(train_y, pred_train)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_test = model.predict(test_x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True, False, False, False,  True,  True,  True, False, False,\n",
       "       False,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True, False,  True])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_y == pred_test  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7878787878787878"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(test_y, pred_test)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_c = test_x[test_y == pred_test]\n",
    "test_f = test_x[test_y != pred_test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x=test_c[:, 0], y=test_c[:, 1], c=test_y[test_y == pred_test],\n",
    "            marker='o', cmap='coolwarm')\n",
    "plt.scatter(x=test_f[:, 0], y=test_f[:, 1], c=test_y[test_y != pred_test],\n",
    "            marker='x', cmap='coolwarm');\n",
    "# plt.savefig('../../images/ch13/ml_plot_07.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins = np.linspace(-4.5, 4.5, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xd = np.digitize(X, bins=bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[34, 21],\n",
       "       [23, 21],\n",
       "       [17, 18],\n",
       "       [31, 15],\n",
       "       [25, 29]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xd[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x, test_x, train_y, test_y = train_test_split(Xd, y, test_size=0.33,\n",
    "                                                    random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  kernel | accuracy\n",
      "--------------------\n",
      "  linear |    0.848\n",
      "    poly |    0.818\n",
      "     rbf |    0.788\n",
      " sigmoid |    0.455\n"
     ]
    }
   ],
   "source": [
    "print('{:>8s} | {:8s}'.format('kernel', 'accuracy'))\n",
    "print(20 * '-')\n",
    "for kernel in ['linear', 'poly', 'rbf', 'sigmoid']:\n",
    "    model = SVC(C=1, kernel=kernel)\n",
    "    model.fit(train_x, train_y)\n",
    "    acc = accuracy_score(test_y, model.predict(test_x))\n",
    "    print('{:>8s} | {:8.3f}'.format(kernel, acc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>"
   ]
  }
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